Q. 174.2( 156 Votes )

A stone is allowe

Answer :


According to Figure the height of tower is 100m, Assuming the two stones meet at point P which is at a height x from the ground, from this we get that distance between Point P and the top of tower is (100-x)

(i)Firstly, for the stone falling from top of tower:

Height, h = (100 - x)

Initial velocity, u = 0

Time, t =?

g = 10 m/s2 (As the stone is falling down)

We know that,


Putting the values in above equation

(100 – x) = 0 × t +1/2× 10 × t2

(100 - x) =  5t2 (i)

(ii)Now, for stone projected vertically upwards:

Height, h = x

Initial velocity, u = 25 m/s

Time, t =?

g = -10 m/s2 (As the stone is going up)


We know that,



Putting the values in above equation

x= 25×t+1/2×(-10)×t2

x = 25t –  5t2 (ii)


Now, by adding (i) and (ii), we get:


100 – x + x =  5t2 + 25 t –  5t2

100 = 25 t

t =

t = 4 s

Therefore, the 2 stones will meet after a time of 4 seconds.

Now, putting the value of t in (i), we get:

100 – x =  5× (4)2

100 – x =  5× 16

100 – x = 80

100 – 80 = x

x = 20m

Therefore, the two stones will meet at a height of 20 m above the ground after 4 seconds

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